REGULAR PAPER

Japanese Journal of Applied Physics 55, 067302 (2016)
http://doi.org/10.7567/JJAP.55.067302

Effect of holed reﬂector on acoustic radiation force
in noncontact ultrasonic dispensing of small droplets
Hiroki Tanaka1*, Yuji Wada2, Yosuke Mizuno1, and Kentaro Nakamura1
1

Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Faculty of Science and Technology, Seikei University, Musashino, Tokyo 180-8633, Japan2*E-mail: htanaka@sonic.pi.titech.ac.jp
Received October 8, 2015; accepted April 11, 2016; published online May 31, 2016
We investigated the fundamental aspects of droplet dispensing, which is an important procedure in the noncontact ultrasonic manipulation ofdroplets in air. A holed reﬂector was used to dispense a droplet from a 27.4 kHz standing-wave acoustic ﬁeld to a well. First, the relationshipbetween the hole diameter of the reﬂector and the acoustic radiation force acting on a levitated droplet was clariﬁed by calculating the acoustic
impedance of the point just above the hole. When the hole diameter was half of (or equal to) the acoustic wavelength λ, the acoustic radiation force
was >80% (or 50%) of that without a hole. The maximal diameters of droplets levitated above the holes through ﬂat and half-cylindrical reﬂectors
were then experimentally investigated. For instance, with the half-cylindrical reﬂector, the maximal diameter was 5.0 mm for a hole diameter of
6.0 mm, and droplets were levitatable up to a hole diameter of 12 mm (>λ). © 2016 The Japan Society of Applied Physics

1.

Introduction

The noncontact transport of small components, powders,and droplets is an increasingly important technology in thepharmaceutical industry as well as in new material scienceand engineering. To date, various methods, such as thoseusing air pressure1) and magnetic=electric ﬁelds,2,3) have beenstudied. Compared with these methods, ultrasonic levitation,
which is based on the phenomenon of objects much smaller
than the wavelength of an acoustic standing wave being
trapped at the nodal points of the pressure ﬁeld, has several
important advantages, such as tranquility, cost eﬃciency, andapplicability to nonelectric=magnetic objects, and thus, it
has attracted considerable attention.4–11) In the meantime, theultrasonic manipulation of small particles or cells in liquid
has been extensively studied by many research groups.12–14)
Our research goal is to implement all the procedures ofnoncontact transport of objects (especially droplets) in air
based on ultrasonics, to wit, injection, linear transport, direction switching, mixing, ejection, analysis, and dispensing, asshown in Fig. 1. We can utilize a variety of ultrasonic technologies to handle small objects in air.15–23) Although linear
transport,24–26) direction switching,27) mixing,28) and ejection29) have already been demonstrated, the other procedures
need to be studied to accomplish the goal.
We here focus on one of the important procedures of themanipulation, i.e., droplet dispensing, the concept of whichis schematically shown in Fig. 2. A vibrating plate and areﬂector with some holes through it are employed to generate
an ultrasonic standing wave between them, and multiple
droplets are trapped at the nodal points. Then, by turning oﬀ
or lowering the vibration, the droplets are dispensed into a
microplate through the holes on the reﬂector. To realize thisconcept, before performing the simultaneous dispensing ofmultiple droplets, certain fundamental aspects, including theacoustic radiation force acting on an object levitated above asingle hole as well as the maximal diameter of a droplet thatcan be levitated, require clariﬁcation.
In this paper, we report results the of numerical simulationsof the relationship between the hole diameter of a reﬂector
and the acoustic radiation force acting on a levitated droplet,
as well as of an experimental investigation of the maximal

Fig. 1. (Color online) Future vision of noncontact ultrasonic transport ofdroplets.

Fig. 2. (Color online) Conceptual setup of multiple-droplet dispensing
system. BLT: bolt-clamped Langevin-type transducer.

diameters of droplets that can be levitated above holes onreﬂectors with two diﬀerent shapes. First, by applying aﬁnite-element method (FEM) to a model comprising a ﬂat
reﬂector and a transducer, we calculate the acoustic impedance of the point just above a hole, based on which thereﬂectivity of the holed reﬂector is plotted as a function ofhole diameter. The trend of the acoustic radiation force acting
on a levitated object with respect to the hole diameter is theninvestigated. Subsequently, to verify whether the FEM results
hold true even when the disturbance of the acoustic ﬁeld by alevitated object is considered, we experimentally investigate
the minimal vibration velocity of a transducer required tolevitate a polystyrene sphere and the maximal diameter of adroplet levitated just above a hole. Here, we utilize not only

067302-1© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 067302 (2016)

H. Tanaka et al.

expressed as the acoustic pressure divided by the particle
velocity of air in the vertical direction,30) was calculated as afunction of hole diameter. The dependence of the acoustic
impedance above the hole, Zh, on the hole diameter was thencalculated by taking an area-based weighted average using thefollowing equation:
Zh ¼

N
X
L2 ð2n  1Þ
n¼1

(b)

(a)

Fig. 3. (Color online) Axis-symmetric models used in (a) experimentsand (b) simulation.

a ﬂat reﬂector but also a half-cylindrical reﬂector, withwhich higher-pressure standing waves can be excited.26) The
obtained simulation and experimental results are comparedand discussed.
2.

Simulation

To generate acoustic standing waves, the reﬂectivity of thereﬂector needs to be suﬃciently high. We therefore needto investigate the eﬀect of a hole on the reﬂector. Here, using
an FEM (ANSYS Mechanical APDL 14.5), we calculated
the acoustic impedance of the point just above a hole on a
ﬂat reﬂector to investigate the relationship between the holediameter and the acoustic radiation force acting on a levitateddroplet. An axis-symmetrical model containing a ﬂat reﬂector
with a hole and a vibrator was employed, as shown in
Figs. 3(a) and 3(b). (Note that, owing to a high computationalcost, it is practically diﬃcult to employ a non-axis-symmetrical model if a middle-class personal computer is used.)
We assumed a horn of 30.0 mm diameter to be vibrating at
27.4 kHz with a maximal zero-to-peak velocity of 0.75 m=s,
the sound speed in air (c) to be 340 m=s, and the air density ( ρ)to be 1.2 kg=m3. The physical parameters, with the exceptionof the hole diameter of the reﬂector, are treated as constantsbecause the acoustic impedance is aﬀected by the otherparameters, such as the vibrator-reﬂector interval. The squaremesh size for calculation was set to 0.5 mm. The acoustic
impedance at each element just above the hole, which is

(a)

r 2h

Zn ;

ð1Þ

where L is the square mesh size, r h is the hole radius (unit:mm), Z n is the acoustic impedance of the n-th mesh from thesymmetric axis (n ¼ 1; 2; . . . ; N, where N = r h=L).
Figure 4(a) shows the result, in which the horizontal axis
is the product of the wavenumber k and the hole diameter d,and the vertical axis is Zh divided by the speciﬁc acoustic
impedance of air in free space, ρc = 408 kg=m2, so that thevalues on both axes become nondimensional. With increasing
kd, the real part of Zh exceeded its imaginary part at kd ∼ 2,
and then converged to 1, which is similar to that observed forthe radiation impedance with a hole.31) When kd is lower than
1, the imaginary part of the acoustic impedance is dominant,resulting in the total reﬂection of the acoustic waves. This
indicates that the generated standing waves stably levitatea droplet. The thickness of the reﬂector, i.e., the length of
the hole, generally plays a major role in determining thediﬀerence between the acoustic impedance at the outlet ofthe hole and that at the inlet. In this model, the length of thehole (1.0 mm) corresponds to approximately 0.1 × λ, and has
almost no eﬀect on the impedance.
Next, assuming that planar waves are radiated from theend of the horn, we calculated the reﬂectivity of the holed
reﬂector within the diameter range of the horn. For thispurpose, we deﬁned Z r as the absolute value of the acoustic
impedance of the point just above the reﬂector (by more than
0.5 mm), which is averaged over the diameter range of lessthan 30.0 mm. We then plotted Z r as a function of kd, as
shown in Fig. 4(b). Here, Z r was calculated as
Zr ¼

M
X
L2 ð2n  1Þ
n¼1

r 2t

jZn j;

ð2Þ

where r t is the horn radius (unit: mm) and ∣Zn∣ is the absolutevalue of the acoustic impedance of the n-th mesh fromthe symmetric axis (n ¼ 1; 2; . . . ; M, where M = r t=L ). The

(b)

(c)

Fig. 4. (a) Acoustic impedance of the point 0–0.5 mm above the hole, Zh, divided by the speciﬁc acoustic impedance of air (ρc) vs product of thewavenumber k and hole diameter d. The solid and dashed lines indicate real and imaginary parts, respectively. (b) Absolute value of the acoustic impedance ofthe point 0.5 mm above the hole (within the diameter range of less than 30.0 mm), Z r, vs kd. The dashed line indicates the ρc value. (c) Square of the reﬂectivity
R vs kd.

067302-2© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 067302 (2016)

H. Tanaka et al.

(a)

(b)

(c)

Fig. 5. (Color online) (a) Experimental setup for dispensing a single droplet, (b) its cross-sectional view, and (c) measured sound pressure above the hole vsdistance from the BLT horn.

speciﬁc acoustic impedance of air ( ρc), indicated by a dashedline, was equal to Z r when kd = 8. This result indicates thata standing wave cannot be excited when the diameter of theholed reﬂector is larger than 1.3 × λ. When the hole diameter
approached zero, the acoustic impedance converged to thespeciﬁc acoustic impedance of aluminum, which is thematerial used for the reﬂector. The square of the reﬂectivity,
R ¼ ðZr  cÞ=ðZr þ cÞ, was then plotted as a function of kd
using ρc [Fig. 4(c)]. This result agrees with the trend of
the relationship between kd and the acoustic radiation force
Fr acting on a levitated object because Fr correlates with
R.2,32,33) With increasing kd, the levitation force decreased.
For example, when the hole diameter was half the wavelength (kd = 3), the acoustic radiation force was approximately 80% of that without a hole, while when the holediameter was identical to the wavelength (kd = 6), the radiation force was 50% of that without a hole. This result indicates that when the hole diameter is suﬃciently small compared with the wavelength, the generated acoustic ﬁeld is astanding wave, while when the hole diameter becomes larger,
the ﬁeld contains a considerable traveling-wave component,
resulting in a reduced levitation force.
3.

Experiments

Subsequently, we performed an experiment using two typesof reﬂectors, i.e., ﬂat and half-cylindrical reﬂectors. The setupof the former is shown in Fig. 3(a), while the setup and crosssectional view of the latter are depicted in Figs. 5(a) and 5(b),respectively. A bolt-clamped Langevin transducer (BLT),
with a step horn with a step-up ratio of 1.8 and a radiation
surface diameter of 30.0 mm, was driven at 27.4 kHz. An
acrylic half-cylindrical plate of 18 mm radius, through whicha hole was drilled, was employed as a reﬂector.26) Ethanol
was used as a droplet, which was manually injected above thehole with a syringe.
To experimentally determine which of the two nodal
points should be used to levitate a droplet in the dispensing
system, using the half-cylindrical reﬂector, we measured theacoustic pressure distribution along the vertical axis throughthe hole using a 1=8-in. microphone (ACO 7118), when thehorn end was vibrating at a zero-to-peak velocity of 1.25 m=s,
as shown in Fig. 5(c). As this measurement was performed todetermine the position of the levitated object, the disturbanceof the acoustic ﬁeld by the microphone was neglected. The
hole diameter was 7.0 mm. As was expected, two nodal

points were observed. The lower nodal point at D = 10 mm
was selected as the position where the droplet would be
levitated, because the antinode at D = 12 mm was higher insound pressure, leading to a larger acoustic radiation force
and thus a more stable levitation.
To verify the simulation result [Fig. 4(c)], we then experimentally investigated the minimal vibration velocity ofthe transducer required for levitation and the relationshipbetween the hole diameter and the transducer-reﬂector interval. The zero-to-peak vibration velocity was calculated fromthe driving current using the force factor, equal to 0.59 N=V
for this transducer, as measured before the experiment.
Rather than ethanol, a polystyrene sphere of 2.5 mm diameter
was employed in this experiment for the following reasons:(1) it is not nebulized, (2) it has constant volume, mass, andsurface area, and (3) it is suﬃciently light to measure slightchanges in acoustic ﬁeld. Using both types of reﬂectors, thehole diameter was varied from 0 to 12.0 mm in steps of
2.0 mm. The transducer-reﬂector interval was set to three
diﬀerent values with a step of 0.5 mm, for which thepolystyrene sphere was levitated right above the hole withany diameter. Note that objects occasionally avoid being
levitated above a hole.23)
Figures 6(a) and 6(b) show the minimal vibration velocityof the transducer plotted as a function of kd for the ﬂat andhalf-cylindrical reﬂectors, respectively. Points for which thehole diameter was 0 mm were plotted as kd = 0.1. Generally,
the required velocity for the half-cylindrical reﬂector was
lower than that for the ﬂat one, which is valid considering
the results in Ref. 26. As the hole diameter increased, theminimal vibration velocity required to keep the object
levitated also increased. Particularly for the ﬂat reﬂector,
when the hole diameter was larger than half the wavelength(kd = 3), the required velocity was higher than that forsmaller holes. Regardless of reﬂector shape, a higher
vibration velocity was required when kd = 1 than that whenkd = 2, which suggests that some resonance is induced at
kd ∼ 1; a more detailed study regarding this point is needed.
As expected from the simulation of acoustic impedance andreﬂectivity, in order to compensate for the leakage of soundenergy from the hole and maintain the sound intensity, highamplitude vibration is required.
Finally, using the ﬂat and half-cylindrical reﬂectors, we
experimentally investigated the relationship between kd andthe maximal diameter of a droplet levitated above a hole, as

067302-3© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 067302 (2016)

H. Tanaka et al.

Fig. 7. Maximal diameter of the levitatable droplet vs product of thewavenumber k and hole diameter d with the ﬂat and half-cylindricalreﬂectors. The solid curves indicate the trends.

(a)

4.

(b)
Fig. 6. (a) Minimum driving current applied to the BLT vs product of thewavenumber k and hole diameter d with the (a) ﬂat and (b) half-cylindricalreﬂectors. The solid curves indicate the trends.

shown in Fig. 7. Again, points for which the hole diameter
was 0 mm were plotted as kd = 0.1. The droplet was
introduced to the lower nodal point with a syringe. A photograph of the levitated droplet was taken along a horizontal
axis using a high-speed camera, and its diameter was measured. Here, as the droplet was not a complete sphere, for the
direct comparison with the hole diameter, we deﬁned the“diameter” of the droplet as its diameter in the horizontal
plane. We deﬁne the “maximal diameter” of the levitateddroplet as the largest diameter that does not exceed the limit
at which the droplet becomes nebulized or falls oﬀ the nodal
point. The driving current of the transducer and the transducer-reﬂector interval were each adjusted according to thehole diameter. Generally, larger droplets were levitated forthe half-cylindrical reﬂector than for the ﬂat one. When thereﬂector was ﬂat, the vibration velocity required to levitate
the object markedly increased when the hole diameter
exceeded ∼70% of the wavelength. For example, the maximal diameter of a levitatable droplet was 2.5 mm for a holediameter of 6.0 mm (approximately half the wavelength).
However, when the hole diameter was larger than 8 mm(∼70% of the wavelength), droplets were not levitated. These
trends are in good agreement with the simulation result
shown in Fig. 4(c). When the half-cylindrical reﬂector wasused, the required vibration velocity increased gradually,
regardless of the hole diameter. The maximal diameter ofa levitatable droplet was, for instance, 5.0 mm for a holediameter of 6.0 mm; a droplet was levitatable when the holediameter was up to 12 mm, which is close to the wavelength.

Conclusions

The basic aspects of one of the most important proceduresof noncontact ultrasonic manipulation of droplets in air —droplet dispensing — were investigated. First, using an FEM,
we numerically analyzed the relationship between the holediameter of a reﬂector and the acoustic radiation force acting
on a levitated droplet. In this simulation, we calculated theacoustic impedance at the point just above a hole and thereﬂectivity of the holed reﬂector, and investigated the relationship between the applied acoustic radiation force and thehole diameter. As a result, it was found that when the holediameter was half of (or equal to) the acoustic wavelength,
the acoustic radiation force was ∼80% (or 50%) of that in
the absence of a hole. Subsequently, the maximal diametersof droplets levitated above holes through ﬂat and halfcylindrical reﬂectors were experimentally investigated. With
the ﬂat reﬂector, the maximal diameter was 2.5 mm for a holediameter of 6.0 mm (approximately half the wavelength);when the hole diameter was larger than 8 mm (approximately
70% of the wavelength), no droplet was levitated. In contrast,with the half-cylindrical reﬂector, the maximal diameter was
5.0 mm for a hole diameter of 6.0 mm, and a droplet waslevitatable up to the hole diameter of 12 mm, which is close
to the wavelength. We believe that these results will be usefulin the development of noncontact ultrasonic droplet dispensers, providing signiﬁcant information for the demonstration of the simultaneous dispensing of multiple droplets
and thus for the realization of noncontact ultrasonic transportsystems in the future.
Acknowledgment

This work was partially supported by JSPS KAKENHI Grant
Number 26289054.

1) S. Konishi, M. Harada, Y. Ogami, Y. Daiho, Y. Mita, and H. Fujita, ETFA
6th Int. Conf., 1997, p. 232.
2) S. Mukhopadhyay, J. Donaldson, G. Sengupta, S. Yamada, C. Chakraborty,
and D. Kacprzak, IEEE Trans. Magn. 39, 3220 (2003).
3) F. Hellman, E. M. Gyorgy, D. W. Johnson, H. M. O’Bryan, and R. C.
Sherwood, J. Appl. Phys. 63, 447 (1988).
4) R. R. Whymark, Ultrasonics 13, 251 (1975).
5) E. G. Lierke, Acustica 82, 220 (1996).
6) H. Hatano, Y. Kanai, Y. Ikegami, T. Fujii, and K. Sato, Nippon Onkyo
Gakkaishi 47, 40 (1991) [in Japanese].
7) E. Benes, M. Groschl, H. Nowotny, F. Trampler, T. K. Keijzer, H. Bohm, S.

067302-4© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 067302 (2016)

8)
9)
10)
11)
12)
13)

14)
15)
16)
17)
18)
19)

H. Tanaka et al.

Radel, L. Gherardini, J. J. Hawkes, R. Konig, and Ch. Delouvroy, Proc.
IEEE Ultrasonics Symp., 2001, p. 649.
Y. Hashimoto, Y. Koike, and S. Ueha, J. Acoust. Soc. Am. 103, 3230
(1998).
Y. Hashimoto, Y. Koike, and S. Ueha, J. Acoust. Soc. Am. 100, 2057
(1996).
R. Yano, M. Aoyagi, H. Tamura, and T. Takano, Jpn. J. Appl. Phys. 50,
07HE29 (2011).
Y. Yamayoshi and S. Hirose, Jpn. J. Appl. Phys. 50, 07HE28 (2011).
T. Kozuka, K. Yasui, S. Hatanaka, T. Tuziuti, K. Suzuki, and A. Towata,
Jpn. J. Appl. Phys. 50, 07HE27 (2011).
K. Masuda, R. Nakamoto, N. Watarai, R. Koda, Y. Taguchi, T. Kozuka, Y.
Miyamoto, T. Kakimoto, S. Enosawa, and T. Chiba, Jpn. J. Appl. Phys. 50,
07HF11 (2011).
M. Takeuchi and K. Yamanouchi, Jpn. J. Appl. Phys. 33, 3045 (1994).
A. Haake and J. Dual, Ultrasonics 42, 75 (2004).
T. Kozuka, K. Yasui, T. Tuziuti, A. Towada, and Y. Iida, Jpn. J. Appl.
Phys. 46, 4948 (2007).
T. Kozuka, K. Yasui, T. Tuziuti, A. Towada, and Y. Iida, Jpn. J. Appl.
Phys. 47, 4336 (2008).
J. Hawkes, J. Cefai, D. Barrow, W. Coakley, and L. Briarty, J. Phys. D 31,
1673 (1998).
W. Coakley, J. Hawkes, M. Sobanski, C. Cousins, and J. Spengler,
Ultrasonics 38, 638 (2000).

20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)

32)
33)

067302-5

A. Haake and J. Dual, J. Acoust. Soc. Am. 117, 2752 (2005).
A. Osumi, K. Doi, and Y. Ito, Jpn. J. Appl. Phys. 50, 07HE30 (2011).
K. Matsumoto and H. Miura, Jpn. J. Appl. Phys. 51, 07GE05 (2012).
H. Tanaka, Y. Wada, Y. Mizuno, and K. Nakamura, Jpn. J. Appl. Phys. 52,
100201 (2013).
D. Koyama and K. Nakamura, IEEE Trans. Ultrason. Ferroelectr. Freq.
Control 57, 1152 (2010).
Y. Ito, D. Koyama, and K. Nakamura, Acoust. Sci. Technol. 31, 420 (2010).
M. Ding, D. Koyama, and K. Nakamura, Appl. Phys. Express 5, 097301(2012).
D. Koyama and K. Nakamura, IEEE Trans. Ultrason. Ferroelectr. Freq.
Control 57, 1434 (2010).
S. Murakami, D. Koyama, and K. Nakamura, AIP Conf. Proc. 1433, 783(2011).
R. Nakamura, Y. Mizuno, and K. Nakamura, Jpn. J. Appl. Phys. 52,
07HE02 (2013).
J. R. Frederick, Ultrasonic Engineering (Wiley, New York, 1965) p. 27.
S. Nishiyama, K. Ikegaya, Z. Yamaguchi, and M. Okujima, Onkyo Shindo
Kogaku (Acoustic and Vibration Engineering) (Corona, Tokyo, 1979) p. 67[in Japanese].
L. P. Gor’kov, Sov. Phys. Dokl. 6, 773 (1962).
T. Kamakura, Hisenkei Onkyo: Kiso to Oyo (Nonlinear Acoustics:
Fundamentals and Applications) (Corona, Tokyo, 2014) [in Japanese].

© 2016 The Japan Society of Applied Physics